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opposite number
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(Definition)
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The opposite number of a number $a$ is such a number $-a$ , that $$-a\!+\!a = 0.$$
Some properties:
- $-0 = 0$
- $-(-a) = a$
- $-(a\!+\!b) = (-a)\!+\!(-b)$
- $-(a\!\cdot\!b) = a\!\cdot\!(-b) = (-a)\!\cdot\!b$
- $-(a\!-\!b) = b\!-\!a$
- $-\sum_{j = 1}^n a_j = \sum_{j = 1}^n (-a_j)$
- $-\int_a^b f(x)\,dx = \int_b^a f(x)\,dx$
Exactly similar properties (except the last) are valid in every ring. The fourth property implies the
Corollary. If one changes the sign of one factor of a ring product, then the sign of the whole product changes.
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"opposite number" is owned by pahio.
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Cross-references: product, ring product, factor, implies, ring, similar, properties, number
There are 12 references to this entry.
This is version 5 of opposite number, born on 2005-02-18, modified 2006-12-08.
Object id is 6775, canonical name is OppositeNumber.
Accessed 14422 times total.
Classification:
| AMS MSC: | 12D99 (Field theory and polynomials :: Real and complex fields :: Miscellaneous) | | | 97D99 (Mathematics education :: Education and instruction in mathematics :: Miscellaneous) |
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Pending Errata and Addenda
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